Resumen de Some Grothendieck's problems in the context of the alfa-pq-tensor products

María José Rivera Ortún , Juan Antonio López Molina

• The positive and negative results related to the problem of topologies of Grothendieck [2] have given many information on the projective and injective tensor products of Fréchet and DF-spaces. The purpose of this paper is to give some results about analogous questions in apq-Lapresté's tensor products [4, chapitre 1] and in spaces of dominated operators Pietsch [5] for a class of Fréchet spaces having a certain kind of decomposition studied dy Bonet and Díaz [1] called T-decomposition. After that we present the main results in order to give positive answers to the following problems:

  P1) To localize the bounded sets in Ea Ä F.

  P2) If E and F are DF-spaces, is Ea'pq Ä F a DF-space?